Question

What irrational number can be added to pi to get a sum that is rational

Answer 1

Answer is  -pi

Let x be this unknown number. Adding on x to pi gets us the expression x+pi

If we set x+pi equal to zero (which is a rational number) and solve for x, we get

x+pi = 0

x+pi - pi = 0 - pi

x = -pi

so adding pi to -pi will lead to 0 since

x+pi = -pi+pi = 0